A Stochastic Perspective on a Group Decision-Making Method Based on Two-Dimension 2-Tuple Linguistic Information

The two-dimension 2-tuple linguistic (TD2L) label, based on the traditional 2-tuple linguistic representation model, adds another 2-tuple linguistic term to express the reliability degree of the assessments. However, the reliability degree is a subjective evaluation on reliability of the given assessments and variables due to the limitations in cognitions and the complexity of decision objects. All assessments without total reliability degree are viewed as uncertain ones. Based on this idea, this paper proposes a new TD2L representation model from a stochastic perspective. The assessment expressed by TD2L is a variable that fluctuates around the given linguistic term, and the fluctuation range is decided by the reliability of the assessment. Therefore, the assessments are regarded as stochastic variables, where the expectancy and deviation of the stochastic variable are corresponding to the first dimension and the second dimension information of TD2Ls, respectively. Consequently, two new aggregation functions for aggregating TD2L labels based on the algorithms among stochastic variables are proposed. In addition, the comparison and similarity measure between TD2L labels are developed, which considers the relative importance of the two dimensions of TD2L labels. Finally, the proposed method is applied to an investment decision of medium sized enterprise and alternatives ranking is provided with the probability of superiority. A comparison analysis conducted from three aspects illustrates the effectiveness of the proposed method.